Finite Group Databasebeta

← #25968871

Subgroups — #25968871

Order 11008.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2C22×#13063316C211yesmaximal, characteristic, complemented
3#19145800C212yesmaximal, complemented
4#19145798C212yesmaximal, complemented
5#19145784C212yesmaximal, complemented
6#19145782C212yesmaximal, complemented
7#19145768C212yesmaximal, complemented
8#19145766C212yesmaximal, complemented
9#19145762C212yesmaximal, complemented
10#19145760C212yesmaximal, complemented
11#19145145C212yesmaximal, complemented
12#19144993C212yesmaximal, complemented
13#19144520C211yesmaximal, characteristic, complemented
14#19144518C211yesmaximal, characteristic, complemented
15#19144515C211yesmaximal, characteristic, complemented
16#19144416C212yesmaximal, complemented
17#19144415C212yesmaximal, complemented
18#19143224C211yesmaximal, characteristic, complemented
19C43×#3092C211yesmaximal, characteristic, complemented
20#14583452C2211yescharacteristic
21#14583451C2211yescharacteristic
22#14583451C2211yescharacteristic
23#14583445C2211yescharacteristic
24#14583444C2211yescharacteristic
25#14583444C2211yescharacteristic
26#14583435C2211yescharacteristic
27#14583435C2211yescharacteristic
28#14583430C2211yescharacteristic
29#14583430C2211yescharacteristic
30#14583429—21no—
31#14583429—21no—
32#14583426—21no—
33#14583426—21no—
34C2×#13063316—21no—
35C2×#13063316—21no—
36C2×#13063316—21no—
37C2×#13063316—21no—
38C2×#13063316—21no—
39C2×#13063316—21no—
40C2×#13063316C2212yes—
41C2×#13063316C2212yes—
42C2×#13063316C2212yes—
43C2×#13063316C2212yes—
44C2×#13063316C2212yes—
45C2×#13063316C2212yes—
46#14583410C2211yescharacteristic
47#14583405—21no—
48#14583405—21no—
49#41×Dic43C2211yescharacteristic
50#14583367C2211yescharacteristic
51C4×#10621900—21no—
52C4×#10621900—21no—
53C22×C4⋊Dic43—21no—
54C22×C4⋊Dic43C2211yescharacteristic
55C22×Dic43⋊C4—21no—
56C22×C4×Dic43C2211yescharacteristic
57#14583307C2214yescomplemented
58#14583306C2214yescomplemented
59#14583300C2214yescomplemented
60#14583299C2214yescomplemented
61#14583266C2214yescomplemented
62#14583262C2214yescomplemented
63#14583255C2214yescomplemented
64#14583252C2214yescomplemented
65#14583235C2212yes—
66#14583234C2212yes—
67#14583232C2212yes—
68#14583230C2212yes—
69#14583229C2212yes—
70#14583227C2212yes—
71#14583218C2212yes—
72#14583217C2212yes—
73#14583215C2212yes—
74#14583213C2212yes—
75#14583212C2212yes—
76#14583210C2212yes—
77#14583209C2214yescomplemented
78#14583208C2214yescomplemented
79#14583205C2214yescomplemented
80#14583204C2214yescomplemented
81#14583202C2214yescomplemented
82#14583201C2214yescomplemented
83#14583198C2214yescomplemented
84#14583197C2214yescomplemented
85#14582953C2212yes—
86#14582953C2212yes—
87#14582949C2212yes—
88#14582949C2212yes—
89#14582942C2212yes—
90#14582941C2212yes—
91#14582939C2212yes—
92#14582922C2212yes—
93#14582901C2212yes—
94#14582900C2212yes—
95#14582898C2212yes—
96#14582863C2211yescharacteristic
97M16×Dic43C2212yes—
98C43×#525C2211yescharacteristic
99C22×C4⋊C4×C43C2211yescharacteristic
100C43×#484C2212yes—
101C43×#483C2212yes—
102C43×#481C2212yes—
103C43×#480C2212yes—
104C43×#428C2212yes—
105C43×#417C2212yes—
106C43×#407C2211yescharacteristic
107C2×#10621898C2311yescharacteristic
108C2×#10621900—21no—
109C2×#10621900—21no—
110C23×Dic43—21no—
111C23×Dic43D411yescharacteristic
112C23×Dic43D411yescharacteristic
113C2×#10621877C2312yes—
114#13063324C2311yescharacteristic
115#13063324C2311yescharacteristic
116#13063323C2311yescharacteristic
117#13063321C2311yescharacteristic
118#13063320—21no—
119#13063320—21no—
120#13063318—21no—
121#13063318—21no—
122#13063316—22no—
123#13063316—22no—
124#13063316—22no—
125#13063316—22no—
126#13063316—22no—
127#13063316—22no—
128#13063316—22no—
129#13063316—22no—
130#13063316—22no—
131#13063316—22no—
132#13063316—22no—
133#13063316—22no—
134#13063316C2311yescharacteristic
135#13063316C2314yes—
136#13063316C2311yescharacteristic
137#13063316C2314yes—
138#13063316C2314yes—
139#13063316C2314yes—
140#13063315—21no—
141#13063315—21no—
142#13063314C2311yescharacteristic
143#13063312C2311yescharacteristic
144#13063311—21no—
145#13063311—21no—
146#13063309—21no—
147#13063309—21no—
148#13063308—21no—
149#13063306—21no—
150#13063306—21no—
151#13063304C2311yescharacteristic
152#13063304C2311yescharacteristic
153#13063302—21no—
154#13063302—21no—
155#13063302—21no—
156#13063302—21no—
157#13063299C2311yescharacteristic
158#13063299C2311yescharacteristic
159#13063297—21no—
160#13063297—21no—
161#13063297—21no—
162#13063297—21no—
163#13063294—21no—
164Q8×Dic43C2311yescharacteristic
165Q8×Dic43C2311yescharacteristic
166C4×Dic86—21no—
167C4×Dic86—21no—
168#13063290—21no—
169#13063290—21no—
170#13063290C2311yescharacteristic
171#13063290C2311yescharacteristic
172D4×Dic43—21no—
173D4×Dic43—21no—
174D4×Dic43—21no—
175D4×Dic43—21no—
176D4×Dic43C2311yescharacteristic
177D4×Dic43C2311yescharacteristic
178#13063287C2311yescharacteristic
179#13063287C2311yescharacteristic
180C4×C22⋊D43—21no—
181C4×C22⋊D43—21no—
182C4×C22⋊D43—21no—
183C4×C22⋊D43—21no—
184(C22⋊D43)⋊C4—21no—
185(C22⋊D43)⋊C4—21no—
186(C22⋊D43)⋊C4—21no—
187(C22⋊D43)⋊C4—21no—
188(C22⋊D43)⋊C4—21no—
189(C22⋊D43)⋊C4—21no—
190#13063284—21no—
191#13063284C2311yescharacteristic
192#13063283—21no—
193#13063283—21no—
194#13063282—21no—
195#13063281—21no—
196#13063281—21no—
197#13063281—21no—
198#13063281—21no—
199C2×C4⋊Dic43—21no—
200C2×C4⋊Dic43—21no—
201C2×C4⋊Dic43—21no—
202C2×C4⋊Dic43—22no—
203C2×C4⋊Dic43—22no—
204C2×C4⋊Dic43—22no—
205C2×C4⋊Dic43—22no—
206C2×C4⋊Dic43—22no—
207C2×C4⋊Dic43—22no—
208C2×C4⋊Dic43C2312yes—
209C2×C4⋊Dic43C2312yes—
210C2×C4⋊Dic43C2312yes—
211C2×Dic43⋊C4—22no—
212C2×Dic43⋊C4—22no—
213C2×Dic43⋊C4—22no—
214C2×Dic43⋊C4—22no—
215C2×Dic43⋊C4—22no—
216C2×Dic43⋊C4—22no—
217C2×C4×Dic43—21no—
218C2×C4×Dic43D411yescharacteristic
219C2×C4×Dic43D411yescharacteristic
220C2×C4×Dic43D411yescharacteristic
221C2×C4×Dic43D411yescharacteristic
222C2×C4×Dic43D411yescharacteristic
223C2×C4×Dic43D411yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C2×C4×Dic43C2311yescharacteristic
226C2×C4×Dic43C2311yescharacteristic
227C2×C4×Dic43C2311yescharacteristic
228C2×C4×Dic43C2311yescharacteristic
229C2×C4×Dic43C2311yescharacteristic
230C42×D43—21no—
231#13063259C2314yes—
232#13063258C2314yes—
233#13063258C2314yes—
234#13063257C2314yes—
235#13063256C2314yes—
236#13063256C2314yes—
237Dic43⋊C8C2314yes—
238Dic43⋊C8C2314yes—
239#13063250C2314yes—
240#13063249C2314yes—
241#13063248C2314yes—
242#13063247C2314yes—
243#13063246C2314yes—
244#13063245C2314yes—
245C22⋊(C43⋊C8)C2312yes—
246C22⋊(C43⋊C8)C2312yes—
247#13063235C2314yes—
248C8×Dic43C2314yes—
249C2×#41×C43C2311yescharacteristic
250C23×C4×C43—21no—
251C23×C4×C43C2311yescharacteristic
252C2×M16×C43C2312yes—
253#123×C43—21no—
254C22⋊Q8×C43C2311yescharacteristic
255C22⋊Q8×C43C2311yescharacteristic
256#121×C43C2311yescharacteristic
257#121×C43C2311yescharacteristic
258#120×C43—21no—
259C4×D4×C43—21no—
260C4×D4×C43—21no—
261#117×C43C2311yescharacteristic
262C2×C4⋊C4×C43—21no—
263C2×C4⋊C4×C43—21no—
264C2×C4⋊C4×C43—21no—
265C2×C4⋊C4×C43C2312yes—
266C2×C4⋊C4×C43C2312yes—
267C2×C4⋊C4×C43C2312yes—
268#107×C43C2314yes—
269#106×C43C2314yes—
270#103×C43C2314yes—
271#102×C43C2314yes—
272C22⋊C8×C43C2312yes—
273C22⋊C8×C43C2312yes—
274C24×C43C2×D411yescharacteristic
275#41×C43—24no—
276C2×Q8×C43C2411yescharacteristic
277C2×D4×C43—21no—
278C2×D4×C43—21no—
279C2×D4×C43—21no—
280C2×D4×C43C2411yescharacteristic
281C22×C4×C43—24no—
282C22×C4×C43—21no—
283C22×C4×C43—22no—
284C22×C4×C43—22no—
285C22×C4×C43—22no—
286C22×C4×C43—44no—
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C2×C22⋊D43—21no—
294C2×C22⋊D43—21no—
295C2×C22⋊D43—21no—
296C2×C22⋊D43—21no—
297C2×C22⋊D43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—22no—
301C22×Dic43—22no—
302C22×Dic43—22no—
303C22×Dic43—42no—
304C22×Dic43—42no—
305C22×Dic43—44no—
306C22×Dic43C2×D411yescharacteristic
307C22×Dic43C2×D411yescharacteristic
308C22×Dic43C2×D411yescharacteristic
309C22×Dic43C2×D411yescharacteristic
310C22×Dic43C2×D411yescharacteristic
311C22×Dic43C2×D411yescharacteristic
312C22×Dic43C2×D411yescharacteristic
313C22×Dic43C2×D411yescharacteristic
314C22×Dic43C2×D411yescharacteristic
315C22×Dic43C2×D411yescharacteristic
316C22×Dic43C2×D411yescharacteristic
317C22×Dic43C2×D411yescharacteristic
318#10621900—44no—
319#10621900—44no—
320#10621898—24no—
321C2×D172C2411yescharacteristic
322C2×C4×D43—21no—
323C2×C4×D43—21no—
324C2×C4×D43—21no—
325C2×Dic86—21no—
326C2×Dic86—21no—
327C2×Dic86C2411yescharacteristic
328M16×C43—24no—
329C2×C8×C43C2414yes—
330C4⋊C4×C43—22no—
331C4⋊C4×C43—22no—
332C4⋊C4×C43—22no—
333C4⋊C4×C43—21no—
334C4⋊C4×C43—21no—
335C4⋊C4×C43C2414yes—
336C4⋊C4×C43C2411yescharacteristic
337C4⋊C4×C43C2411yescharacteristic
338C22⋊C4×C43—21no—
339C22⋊C4×C43—21no—
340C22⋊C4×C43—21no—
341C22⋊C4×C43—21no—
342C22⋊C4×C43—21no—
343C42×C43—21no—
344C22⋊Dic43—21no—
345C22⋊Dic43—21no—
346C22⋊Dic43—21no—
347C22⋊Dic43—21no—
348C22⋊Dic43—21no—
349C22⋊Dic43—21no—
350C22⋊Dic43—21no—
351(C2×D43)⋊C4—21no—
352(C2×D43)⋊C4—21no—
353(C2×D43)⋊C4—21no—
354(C2×D43)⋊C4—21no—
355(C2×D43)⋊C4—21no—
356(C2×D43)⋊C4—21no—
357C4⋊Dic43—22no—
358C4⋊Dic43—22no—
359C4⋊Dic43—22no—
360C4⋊Dic43—24no—
361C4⋊Dic43—24no—
362C4⋊Dic43—24no—
363C4⋊Dic43—24no—
364C4⋊Dic43—21no—
365C4⋊Dic43—21no—
366C4⋊Dic43—21no—
367C4⋊Dic43—21no—
368C4⋊Dic43C2414yes—
369C4⋊Dic43C2411yescharacteristic
370C4⋊Dic43C2411yescharacteristic
371Dic43⋊C4—21no—
372Dic43⋊C4—21no—
373Dic43⋊C4—24no—
374Dic43⋊C4—24no—
375Dic43⋊C4—24no—
376Dic43⋊C4—24no—
377Dic43⋊C4—21no—
378Dic43⋊C4—21no—
379Dic43⋊C4—21no—
380Dic43⋊C4—21no—
381Dic43⋊C4—21no—
382Dic43⋊C4—21no—
383Dic43⋊C4—21no—
384Dic43⋊C4—21no—
385C4×Dic43—21no—
386C4×Dic43—21no—
387C4×Dic43—21no—
388C4×Dic43—21no—
389C4×Dic43—21no—
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2×D411yescharacteristic
392C4×Dic43C2×D411yescharacteristic
393C4×Dic43C2×D411yescharacteristic
394C4×Dic43C2×D411yescharacteristic
395C4×Dic43C2×D411yescharacteristic
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2×D411yescharacteristic
399C4×Dic43C2×D411yescharacteristic
400C4×Dic43C2×D411yescharacteristic
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2411yescharacteristic
403C4×Dic43C2411yescharacteristic
404C4×Dic43C2411yescharacteristic
405C4×Dic43C2411yescharacteristic
406#10621877—24no—
407C2×C43⋊C8C2414yes—
408C23×C43—22no—
409C23×C43—22no—
410C23×C43—22no—
411C23×C43—21no—
412C23×C43C22×D411yescharacteristic
413C23×C43C22×D411yescharacteristic
414C23×C43C22×D411yescharacteristic
415C22×D43—21no—
416Q8×C43—22no—
417D4×C43—22no—
418D4×C43—42no—
419D4×C43—42no—
420D4×C43—42no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—21no—
427C2×C4×C43—21no—
428C2×C4×C43—21no—
429C2×C4×C43—24no—
430C2×C4×C43—44no—
431C2×C4×C43—44no—
432C2×C4×C43—44no—
433C2×C4×C43—42no—
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C432−1+414yes—
438C2×C4×C43C2511yescharacteristic
439C22⋊D43—42no—
440C22⋊D43—42no—
441C22⋊D43—42no—
442C22⋊D43—42no—
443C22⋊D43—42no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—21no—
449C2×Dic43—21no—
450C2×Dic43—21no—
451C2×Dic43—24no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—42no—
461C2×Dic43—42no—
462C2×Dic43—44no—
463C2×Dic43—44no—
464C2×Dic43—44no—
465C2×Dic43C22×D411yescharacteristic
466C2×Dic43C22×D411yescharacteristic
467C2×Dic43C22×D411yescharacteristic
468C2×Dic43C22×D411yescharacteristic
469C2×Dic43C22×D411yescharacteristic
470C2×Dic43C22×D411yescharacteristic
471C2×Dic43C22×D411yescharacteristic
472C2×Dic43C22×D411yescharacteristic
473D172—22no—
474C4×D43—42no—
475C4×D43—42no—
476C4×D43—42no—
477Dic86—22no—
478Dic86—42no—
479Dic86—42no—
480C8×C43—24no—
481C43⋊C8—24no—
482#60861—431nomaximal, Sylow
483C22×C43—28no—
484C22×C43—21no—
485C22×C43—21no—
486C22×C43—21no—
487C22×C43—21no—
488C22×C43—21no—
489C22×C43—21no—
490C22×C43—41no—
491C22×C43—41no—
492C22×C43—41no—
493C22×C43#53612yes—
494C22×C43#57512yes—
495C22×C43#57512yes—
496C22×C43C23×D411yescharacteristic
497C2×D43—41no—
498C2×D43—41no—
499C2×D43—41no—
500C4×C43—21no—
501C4×C43—21no—
502C4×C43—41no—
503C4×C43—41no—
504C4×C43—41no—
505C4×C43—44no—
506C4×C43#53612yes—
507C4×C43C2×2−1+412yes—
508Dic43—21no—
509Dic43—21no—
510Dic43—21no—
511Dic43—21no—
512Dic43—21no—
513Dic43—21no—
514Dic43—21no—
515Dic43—21no—
516Dic43—41no—
517Dic43—41no—
518Dic43—41no—
519Dic43—44no—
520#3444—431no—
521C22×#125—431no—
522#3236—432no—
523#3236—432no—
524#3234—432no—
525#3234—432no—
526#3232—432no—
527#3232—432no—
528#3232—432no—
529#3232—432no—
530#3166—432no—
531#3142—432no—
532#3092—431no—
533#3092—431no—
534#3092—431no—
535#3092D4311yescharacteristic, complemented
536#3080—432no—
537#3080—432no—
538#2920—431no—
539C2×C43—22no—
540C2×C43—22no—
541C2×C43—22no—
542C2×C43—81no—
543C2×C43C2×#53611yescharacteristic
544C2×C43C2×#57511yescharacteristic
545C2×C43C2×#57511yescharacteristic
546D43—81no—
547#533—431no—
548#533—431no—
549#533—431no—
550#532—431no—
551#532—431no—
552#532—431no—
553#529—431no—
554#529—431no—
555#529—431no—
556#529—431no—
557#529—861no—
558#529—861no—
559#529—861no—
560#529—861no—
561C2×#125—432no—
562C2×#125—432no—
563C2×#125—432no—
564C2×#125—432no—
565C2×#125—432no—
566C2×#125—432no—
567C2×#125—861no—
568C2×#125—861no—
569C2×#125—861no—
570C2×#125—861no—
571C2×#125—861no—
572C2×#125—861no—
573#525—431no—
574#525—861no—
575#525—861no—
576#525C2×D4311yescharacteristic
577C4×#41—431no—
578C4×#41—431no—
579C4×#41—861no—
580C4×#41—861no—
581C22×C4⋊C4—431no—
582C22×C4⋊C4—861no—
583C22×C4⋊C4—861no—
584C22×C4⋊C4C2×D4311yescharacteristic
585C22×C42—431no—
586#501—434no—
587#501—434no—
588#499—434no—
589#499—434no—
590#491—434no—
591#490—434no—
592#488—434no—
593#488—434no—
594#484—432no—
595#484—432no—
596#484—432no—
597#484C2×D4312yes—
598#483—432no—
599#483—432no—
600#483—432no—
601#483C2×D4312yes—
602#481—432no—
603#481—432no—
604#481—432no—
605#481C2×D4312yes—
606#480—432no—
607#480—432no—
608#480—432no—
609#480C2×D4312yes—
610#479—434no—
611#479—434no—
612#479—434no—
613#479—434no—
614#478—434no—
615#478—434no—
616#478—434no—
617#478—434no—
618#432—432no—
619#432—432no—
620#431—432no—
621#431—432no—
622#428—432no—
623#428—432no—
624#428—432no—
625#428C2×D4312yes—
626#423—432no—
627#417—432no—
628#417—432no—
629#417—432no—
630#417C2×D4312yes—
631#407—431no—
632#407C2×D4311yescharacteristic
633C4×M16—432no—
634C43#6086111yescharacteristic, complemented, Sylow
635C2×#41—431no—
636C2×#41—861no—
637C2×#41—861no—
638C2×#41C22×D4311yescharacteristic
639C23×C4—21no—
640C23×C4—431no—
641C23×C4—431no—
642C23×C4—861no—
643C23×C4C22×D4311yescharacteristic
644C2×M16—432no—
645C2×M16C22×D4312yes—
646C4⋊Q8—431no—
647C4⋊Q8—431no—
648C4⋊Q8—431no—
649#127—431no—
650#126—861no—
651#126—861no—
652#126—861no—
653#126—861no—
654#125—434no—
655#125—434no—
656#125—434no—
657#125—434no—
658#125—431no—
659#125—431no—
660#125—862no—
661#125—862no—
662#125—862no—
663#125—862no—
664#125—862no—
665#125—862no—
666#125—862no—
667#125—862no—
668#125—862no—
669#125—862no—
670#125—862no—
671#125—862no—
672#125—861no—
673#125—861no—
674#124—431no—
675#124—431no—
676#124—861no—
677#124—861no—
678#123—21no—
679#123—861no—
680#123—861no—
681#123—861no—
682#123—861no—
683#123—861no—
684C22⋊Q8—431no—
685C22⋊Q8—431no—
686C22⋊Q8—861no—
687C22⋊Q8—861no—
688C22⋊Q8—861no—
689C22⋊Q8—861no—
690C22⋊Q8C22×D4311yescharacteristic
691C22⋊Q8C22×D4311yescharacteristic
692#121—431no—
693#121—431no—
694#121—861no—
695#121—861no—
696#121—861no—
697#121—861no—
698#121C22×D4311yescharacteristic
699#121C22×D4311yescharacteristic
700#120—21no—
701#120—861no—
702C4×Q8—431no—
703C4×Q8—431no—
704C4×Q8—431no—
705C4×Q8—431no—
706C4×Q8—861no—
707C4×Q8—861no—
708C4×Q8—861no—
709C4×Q8—861no—
710C4×D4—21no—
711C4×D4—21no—
712C4×D4—431no—
713C4×D4—431no—
714C4×D4—431no—
715C4×D4—431no—
716C4×D4—861no—
717C4×D4—861no—
718C4×D4—861no—
719C4×D4—861no—
720C4×D4—861no—
721C4×D4—861no—
722C4×D4—861no—
723C4×D4—861no—
724C4×D4—861no—
725C4×D4—861no—
726C4×D4—861no—
727C4×D4—861no—
728C4×D4—861no—
729C4×D4—861no—
730#117—431no—
731#117—861no—
732#117—861no—
733#117—861no—
734#117—861no—
735#117—861no—
736#117—861no—
737#117—861no—
738#117—861no—
739#117C22×D4311yescharacteristic
740C2×C4⋊C4—21no—
741C2×C4⋊C4—21no—
742C2×C4⋊C4—21no—
743C2×C4⋊C4—432no—
744C2×C4⋊C4—432no—
745C2×C4⋊C4—432no—
746C2×C4⋊C4—862no—
747C2×C4⋊C4—862no—
748C2×C4⋊C4—862no—
749C2×C4⋊C4—862no—
750C2×C4⋊C4—862no—
751C2×C4⋊C4—862no—
752C2×C4⋊C4—862no—
753C2×C4⋊C4—862no—
754C2×C4⋊C4—862no—
755C2×C4⋊C4—862no—
756C2×C4⋊C4—862no—
757C2×C4⋊C4—862no—
758C2×C4⋊C4—861no—
759C2×C4⋊C4—861no—
760C2×C4⋊C4—861no—
761C2×C4⋊C4C22×D4312yes—
762C2×C4⋊C4C22×D4312yes—
763C2×C4⋊C4C22×D4312yes—
764C2×C42—431no—
765C2×C42—431no—
766C2×C42—431no—
767C2×C42—431no—
768C2×C42—431no—
769C2×C42—431no—
770C2×C42—431no—
771C2×C42—431no—
772C2×C42—431no—
773C2×C42—431no—
774C2×C42—431no—
775C2×C42—431no—
776C2×C42—861no—
777C2×C42—861no—
778#107—434no—
779#107—434no—
780#107—434no—
781#107C22×D4314yes—
782#106—434no—
783#106—434no—
784#106—434no—
785#106C22×D4314yes—
786C4⋊C8—434no—
787C4⋊C8—434no—
788#103—434no—
789#103—434no—
790#103—434no—
791#103C22×D4314yes—
792#102—434no—
793#102—434no—
794#102—434no—
795#102C22×D4314yes—
796C22⋊C8—432no—
797C22⋊C8—432no—
798C22⋊C8C22×D4312yes—
799C22⋊C8C22×D4312yes—
800#97—434no—
801C4×C8—434no—
802C24D4×D4311yescharacteristic
803#41—24no—
804#41—864no—
805#41—1724no—
806#41—1724no—
807C2×Q8—431no—
808C2×Q8—861no—
809C2×Q8—861no—
810C2×Q8C23×D4311yescharacteristic
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—431no—
815C2×D4—861no—
816C2×D4—861no—
817C2×D4—861no—
818C2×D4—861no—
819C2×D4—861no—
820C2×D4C23×D4311yescharacteristic
821C22×C4—24no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—44no—
827C22×C4—431no—
828C22×C4—431no—
829C22×C4—431no—
830C22×C4—431no—
831C22×C4—431no—
832C22×C4—431no—
833C22×C4—431no—
834C22×C4—431no—
835C22×C4—431no—
836C22×C4—431no—
837C22×C4—431no—
838C22×C4—431no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—862no—
844C22×C4—862no—
845C22×C4—862no—
846C22×C4—861no—
847C22×C4—1722no—
848C22×C4—1722no—
849C22×C4—1724no—
850C22×C4D4×D4311yescharacteristic
851C22×C4D4×D4311yescharacteristic
852C22×C4D4×D4311yescharacteristic
853C22×C4C23×D4311yescharacteristic
854C22×C4C23×D4311yescharacteristic
855C22×C4C23×D4311yescharacteristic
856M16—24no—
857M16—864no—
858C2×C8—434no—
859C2×C8C23×D4314yes—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—434no—
866C4⋊C4—431no—
867C4⋊C4—431no—
868C4⋊C4—864no—
869C4⋊C4—864no—
870C4⋊C4—864no—
871C4⋊C4—864no—
872C4⋊C4—864no—
873C4⋊C4—864no—
874C4⋊C4—864no—
875C4⋊C4—864no—
876C4⋊C4—861no—
877C4⋊C4—861no—
878C4⋊C4—861no—
879C4⋊C4—861no—
880C4⋊C4—861no—
881C4⋊C4—861no—
882C4⋊C4—861no—
883C4⋊C4—861no—
884C4⋊C4—861no—
885C4⋊C4—861no—
886C4⋊C4—861no—
887C4⋊C4—861no—
888C4⋊C4—862no—
889C4⋊C4—862no—
890C4⋊C4—862no—
891C4⋊C4—861no—
892C4⋊C4—861no—
893C4⋊C4C23×D4314yes—
894C4⋊C4C23×D4311yescharacteristic
895C4⋊C4C23×D4311yescharacteristic
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—21no—
899C22⋊C4—21no—
900C22⋊C4—21no—
901C22⋊C4—861no—
902C22⋊C4—861no—
903C22⋊C4—861no—
904C22⋊C4—861no—
905C22⋊C4—861no—
906C22⋊C4—861no—
907C22⋊C4—861no—
908C22⋊C4—861no—
909C22⋊C4—861no—
910C22⋊C4—861no—
911C22⋊C4—861no—
912C22⋊C4—861no—
913C22⋊C4—861no—
914C42—21no—
915C42—431no—
916C42—431no—
917C42—431no—
918C42—431no—
919C42—431no—
920C42—431no—
921C42—431no—
922C42—431no—
923C42—431no—
924C42—431no—
925C42—431no—
926C42—431no—
927C42—431no—
928C42—431no—
929C42—431no—
930C42—431no—
931C42—861no—
932C42—861no—
933C42—861no—
934C42—861no—
935C42—861no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—21no—
940C23—861no—
941C23C2×D4×D4311yescharacteristic
942C23C2×D4×D4311yescharacteristic
943C23C2×D4×D4311yescharacteristic
944Q8—22no—
945Q8—862no—
946Q8—1722no—
947Q8—1722no—
948D4—22no—
949D4—42no—
950D4—42no—
951D4—42no—
952D4—862no—
953D4—1722no—
954D4—1722no—
955D4—1722no—
956D4—1722no—
957D4—1722no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—24no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—42no—
971C2×C4—431no—
972C2×C4—431no—
973C2×C4—431no—
974C2×C4—431no—
975C2×C4—431no—
976C2×C4—431no—
977C2×C4—431no—
978C2×C4—431no—
979C2×C4—862no—
980C2×C4—862no—
981C2×C4—862no—
982C2×C4—862no—
983C2×C4—861no—
984C2×C4—861no—
985C2×C4—861no—
986C2×C4—864no—
987C2×C4—1722no—
988C2×C4—1722no—
989C2×C4—1721no—
990C2×C4—1721no—
991C2×C4—1721no—
992C2×C4—1721no—
993C2×C4—1721no—
994C2×C4—1721no—
995C2×C4—1721no—
996C2×C4—1721no—
997C2×C4—1722no—
998C2×C4—1722no—
999C2×C4—1724no—
1000C2×C4—1724no—
1001C2×C4—1724no—
1002C2×C4—1722no—
1003C2×C4C2×D4×D4311yescharacteristic
1004C2×C4C2×D4×D4311yescharacteristic
1005C2×C4C2×D4×D4311yescharacteristic
1006C2×C4#1306337214yes—
1007C2×C4C24×D4311yescharacteristic
1008C8—24no—
1009C8—864no—
1010C22—28no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—1721no—
1021C22—1721no—
1022C22—1721no—
1023C22#1458347112yes—
1024C22#1458369512yes—
1025C22#1458369812yes—
1026C22C22×D4×D4311yescharacteristic
1027C4—21no—
1028C4—21no—
1029C4—44no—
1030C4—41no—
1031C4—41no—
1032C4—41no—
1033C4—861no—
1034C4—861no—
1035C4—861no—
1036C4—861no—
1037C4—861no—
1038C4—861no—
1039C4—861no—
1040C4—861no—
1041C4—1721no—
1042C4—1724no—
1043C4—1721no—
1044C4—1721no—
1045C4#1458347112yes—
1046C4C2×#1306337212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—81no—
1051C2—3441no—
1052C2C2×#1458347111yescharacteristic
1053C2C2×#1458369511yescharacteristic
1054C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3092C2
socleC22×C43C23×D4
prime radical#19147887C2
hypercenter#3092D43
hypocenterC43#60861
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#13063316C2semidirect
3. #19145800C2semidirect
4. #19145798C2semidirect
5. #19145784C2semidirect
6. #19145782C2semidirect
7. #19145768C2semidirect
8. #19145766C2semidirect
9. #19145762C2semidirect
10. #19145760C2semidirect
11. #19145145C2semidirect
12. #19144993C2semidirect
13. #19144520C2semidirect
14. #19144518C2semidirect
15. #19144515C2semidirect
16. #19144416C2semidirect
17. #19144415C2semidirect
18. #19143224C2semidirect
19. C43×#3092C2semidirect
57. #14583307C22semidirect
58. #14583306C22semidirect
59. #14583300C22semidirect
60. #14583299C22semidirect
61. #14583266C22semidirect
62. #14583262C22semidirect
63. #14583255C22semidirect
64. #14583252C22semidirect
77. #14583209C22semidirect
78. #14583208C22semidirect
79. #14583205C22semidirect
80. #14583204C22semidirect
81. #14583202C22semidirect
82. #14583201C22semidirect
83. #14583198C22semidirect
84. #14583197C22semidirect
535. #3092D43semidirect
634. C43#60861semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191478872
C22×#130633162
#191458002
#191457982
#191457842
#191457822
#191457682
#191457662
#191457622
#191457602
#191451452
#191449932
#191445202
#191445182
#191445152
#191444162
#191444152
#191432242
C43×#30922
#6086143